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Algebra 2 Chapter 7 Review Answer Key Evaluate the expression. 3 1. 8 2. 2 36 1 1 125 3 2 36 6 2 3. 4. 16 1 5. 4 9 125 3 2 1 5 25 2 16 1 4 1 2 Simplify the expression. Assume all variables are positive. 6. 2 14 5 14 2 9. 4 4 5 4 4 4 7. 5 32 x 5 y 5 z 5 32 x 5 21 51 10 5 y 5 5 z 3 48 5 2 xyz 1 1 16 4 16 3 3 25 3 20 3 2 25 20 3 2 4 3 3 3 250 5 3 3 125 2 48 3 5 5 3 48 8. 3 10. 53 2 Perform the indicated operation and state the domain. Let f ( x) x 3 and g ( x) x 1 11. f ( x) g ( x) 12. 13. f ( x) g ( x) x x 1 x ( x 1) x x 1 x 3 x 1 x3 x 1 x4 x3 3 3 Domain: All Real #s 14. f ( x) g ( x) f ( x) g ( x) x 3 ( x 1) Domain: All real #s except – 1 3 Domain: All Real #s Domain: All Real #s 15. 16. f ( g ( x)) f x 1 x 1 3 Domain: All real #s g ( f ( x)) x 1 g x3 3 Domain: All real #s 4 9 3 4 9 1 3 4 4 9 1 2 1 3 Find the inverse function. To find an inverse: 1. Change the f(x) to a y 2. Switch the x and y’s. 3. Solve for y. 4. Change y to a f-1(x) 17. f ( x) 3 x 2 18. f ( x) 3 x6 4 3 x6 4 3 x y6 4 4 4 3 x 6 y 3 3 4 4 ( x 6) y 3 4 ( x 6) f 1 ( x) 3 y y 3x 2 x 3y 2 x 2 3y x2 y 3 x2 f 1 ( x) 3 19. f ( x) x 4 , x 0 20. f ( x) 2 x 3 y 2x 3 x 2y3 y x4 x y3 2 x 3 3 3 y 2 x y4 4 x 4 y4 4 xy 4 x f 1 ( x) 3 x y 2 3 x f 2 1 ( x) Graph the function (not the inverse). Then state the domain and range. Also label the starting point/vertex. 21. f ( x) x 1 4 22. f ( x) 3 x 1 2 23. f ( x) 23 x 3 1 Starting Point: (– 1, 4) Starting Point: (1, 2) Starting Point: (– 3, 1) Domain: All real #s ≥ – 1 Domain: All real #s Domain: All real #s Range: All real #s ≥ 4 Range: All real #s Range: All real #s 24. f ( x) 2 x 2 1 25. f ( x) 33 x 4 6 Starting Point: (2, – 1) Starting Point: (– 4, 6) Domain: All real #s ≥ 2 Domain: All real #s Range: All real #s ≥ – 1 Range: All real #s Solve the equation. Check for extraneous solutions. 26. 4 3x 2 3x 4 2 4 4x x 9 27. 4x 2 4 3x 16 16 x 3 x9 2x 3 x 3 28. 2 2x 3 2 x 3 2 2 x 3 x 3x 3 4x x 9 2x 3 x 2 6x 9 3x 9 0 x 2 8 x 12 0 x 6 x 2 x3 x 6, x 2 Answer checks. Answer checks. After checking, only x = 6 works 29. x2 2 x x2 2 x x2 2 x 2 2 x 2 ( x 2)( x 2) x 2 x 2 4x 4 0 x 2 3x 2 0 ( x 2)( x 1) x 2, x 1 After checking, both work. Chapter test will be half calculator and half non-calculator. Graphing questions will be on the noncalculator part of the test. Be sure you can graph square roots and cube roots by hand! Also, remember how to determine the domain of a function. There are two things not allowed. 1. You cannot divide by 0 2. You cannot take an EVEN root of a NEGATIVE number. Examples: x3 Domain : All real numbers except x = 5. x 5 (If x = 5, you would divide by 0) 2. Find the domain of: x 3/ 4 Domain: All non-negative numbers. 1. Find the domain of: ( x 3/ 4 means x , and you can’t take a 4 4 3 th root of a negative number, but 0 is ok) 3. Find the domain of: x 3/ 4 Domain: All positive real numbers. 1 1 ( x 3/ 4 means 3/4 , and you can’t take a 4th root of a negative number, or 3 4 x x divide by 0, so the domain is all positive real numbers) Remember what function notation means. f(g(x)) is read “f of g of x.” It does not mean “f times g times x.” Be sure to be able to do a composite function. Remember to determine the domain at the start of the problem, not at the end. The ending result does NOT determine the domain! Always check for extraneous solutions. There is a good chance one will appear on your test. Remember that properties of rational exponents are the same as properties of integer exponents.